Space-Time Adaptive Processing
Space-time adaptive processing (STAP) is frequently used in radar systems to detect a target. STAP has been known since the early 1970's. In airborne radar systems, STAP improves target detection when disturbances in an environment, e.g., noise, ground clutter and jamming, are a problem. The disturbances can be Gaussian or non-Gaussian. STAP can achieve order-of-magnitude sensitivity improvements in target detection.
Typically, STAP involves a two-dimensional filtering technique applied to signals received by a phased-array antenna with multiple spatial channels (antennas). Coupling the multiple spatial channels with time dependent pulse-Doppler waveforms leads to STAP. By applying statistics of interference of the environment, a space-time adaptive weight vector is formed. Then, the weight vector is applied to the coherent signals received by the radar to detect the target.
STAP Detector Filter
As shown in FIG. 1 for conventional STAP, observations include a test signal 101, a set of training signals 102, and a steering vector 103. In a homogeneous environment, the test signal shares the same covariance matrix with the training signals.
It is a known problem to detect a moving target from a moving platform in many applications including radar, wireless communications, and hyperspectral imaging acquired across the entire electromagnetic spectrum. STAP can to deal with strong spatially and temporally colored disturbances.
However, the conventional STAP is not suitable for many from practical applications due to excessive training requirements and a high computational complexity, for example, a covariance-matrix-based STAP detectors, which need K, JN training signals to ensure a full-rank estimate of the disturbance covariance matrix and have to invert a JN×JN matrix, where J denotes the number of antennas and N denotes the number of pulses.
As shown in FIG. 1, by modeling the disturbance as a multichannel auto-regressive (AR) process, a parametric STAP detector 100 decompose jointly spatio-temporal whitening of the covariance-matrix-based detectors into successive temporal 110 and spatial 120 whitening by using the estimate of the temporal correlation matrix A 130, and a spatial covariance matrix Q 140, given the test signal 101, training signals 102 and a steering vector 103, where (.)H 145 indicates a Hermitian transpose.
The results of the spatial whitenings 120 are multiplied 149 by each other to produce corresponding sums Σn=PN-1(.) 150, for which the magnitudes |.|2 170 are determined. The magnitudes are divided (/) 175 into each other to determine the test statistic TPAMF 180 of the parametric adaptive matched filter (PAMF). The test statistic 180 is compared to a threshold 190 to obtain a decision 195 whether a target is present or not in the test signal.
Matrix Estimation
As shown in FIG. 2, an estimated temporal correlation matrix A 130 and an estimated of spatial correlation matrix Q 140 are determined 200 as follows:                a regression vector yk (n) 215 is constructed 210 from the training signals xk (n) 102;        using the training signals 102, an estimate of an autocorrelation of the training signal {circumflex over (R)}xx 220 is determined;        using the training signals and the regression vector, an estimate of a cross correlation of yk (n) 215 and xk (n) 102 is determined 240; using the regression vector 215, an estimate of an autocorrelation {circumflex over (R)}yy is determined 230;        an estimate of the spatial covariance matrix Q 140 is determined 250 as        
                                          Q            ^                    =                                                                      R                  ^                                xx                            -                                                                    R                    ^                                    yx                  H                                ⁢                                                      R                    ^                                    yy                                      -                    1                                                  ⁢                                                      R                    ^                                    yx                                                                    K              ⁡                              (                                  N                  -                  P                                )                                                    ⁢                                  ;                    130      and                an estimate of the autoregressive coefficient matrix 130 is determined 260 Â=−{circumflex over (R)}yy−1{circumflex over (R)}yx.        